A_n型路代数倾斜模的一个必要条件

A Necessary Condition of Tilting Modules Over Path Algebras of Type A_n

代数表示理论是上个世纪70年代初兴起的代数学的一个新分支,而倾斜理论是研究代数表示理论的重要工具之一.本文主要对An型路代数倾斜模在其对应的AR-箭图上的结构特点进行研究.通过对An型路代数的AR-箭图分析及利用APR-倾斜变换证明了An型路代数倾斜模TA的一个必要条件是,在A的AR-箭图ΓA的最高τ-轨道与最底τ-轨道都有TA的不可分解直和项对应的点.

Representation theory of algebras is a new branch of algebra which began at the seventies of the last century. Tilting theory is an important tool to study representation theory of algebras. The main purpose of this paper is to study structural character- istics of the tilting module over path algebra of type A, in its AR-quiver. AR-quiver analysis and APR- tilting translation was used to proved that：if TA is a tilting A-module over a path algebra of type An, then there are points corresponding indecomposable direct summands of TA in both the highest τ- orbit and the lowest τ-orbit.